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Tables of crystallographic properties of double antisymmetry space groups, including symmetry element diagrams, general position diagrams, and positions, with multiplicities, site symmetries, coordinates, spin and roto vectors are presented.
Rotation-reversal symmetry was recently introduced to generalize the symmetry classification of rigid static rotations in crystals such as tilted octahedra in perovskite structures and tilted tetrahedral in silica structures. This operation has impor
Distortions are ubiquitous in nature. Under perturbations such as stresses, fields, or other changes, a physical system reconfigures by following a path from one state to another; this path, often a collection of atomic trajectories, describes a dist
Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time-states, position-states, charge-states, spin-states, chemical-species etc. This review covers th
Atomic-scale investigation on mechanical behaviors is highly necessary to fully understand the fracture mechanics especially of brittle materials, which are determined by atomic-scale phenomena (e.g., lattice trapping). Here, exfoliated anisotropic r
Standard X-ray crystallography methods use free-atom models to calculate mean unit cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a charge density